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Prediction of quantiles by statistical learning and application to GDP forecasting

Pierre Alquier 1, 2, Xiaoyin Li 3

(2012-02-12)

In this paper, we tackle the problem of prediction and confidence intervals for time series using a statistical learning approach and quantile loss functions. In a first time, we show that the Gibbs estimator (also known as Exponentially Weighted aggregate) is able to predict as well as the best predictor in a given family for a wide set of loss functions. In particular, using the quantile loss function of Koenker and Bassett (1978), this allows to build confidence intervals. We apply these results to the problem of prediction and confidence regions for the French Gross Domestic Product (GDP) growth, with promising results.

1:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
2:	Centre de Recherche en Économie et Statistique (CREST)
	INSEE – École Nationale de la Statistique et de l'Administration Économique
3:	Laboratoire d'Analyse, Géométrie et Modélisation (AGM)
	CNRS : UMR8088 – Université de Cergy Pontoise

Subject

:

Mathematics/Statistics Statistics/Statistics Theory

Keyword(s): Statistical learning theory – Time series prediction – Quantile regression – GDP forecasting – PAC-Bayesian bounds – Oracle inequalities – Weak dependence – Confidence intervals – Business surveys

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From: Pierre Alquier <>

Submitted on: Monday, 20 February 2012 11:29:31

Updated on: Monday, 20 February 2012 11:35:27